Fig 1.
Liver microstructure and functional units.
The liver representative periodic cell (LRPC) incorporates the Portal lobule and also the Acinus. Functional zones z. 1–3 are indicated.
Fig 2.
The LRPC geometry with descriptions of the PV and HV tracks connected with the central and vertex veins of the lobule.
Fig 3.
Positions of the nodes generating the primary and dual lattices.
Left: The generating unit is defined using unit vectors of the primary and dual bases, {ei} and {gi}, respectively. Right: position of the vertex pk and the central hk points within the generating unit—the portal lobule.
Fig 4.
Left: Portal lobule unit associated with , d = h, p. Middle & Right: The LRPC is obtained by translations, see Eqs (5) and (6), and generate the periodic lattice.
Fig 5.
Generating vessel , see Eq (1).
Table 1.
Transversal vessels , i = 1, 2, 3 of the central vein vasculature.
The structure is generated by three vessels, see Eq (3).
Table 2.
Transversal vessels , j = 1, 2, 3 of the vertex vein vasculature.
The structure is generated by three vessels, see Eq (4).
Fig 6.
Fig 7.
Finite element mesh of the LRPC (right). Decomposition of domain Y (left).
Fig 8.
Liver perfusion simulations for two different orientations of the lobular lattice (upper and lower rows).
The same boundary conditions according to Eq (11) are prescribed in both cases, whereby surfaces Γp and Γh form opposite sides of the specimen. Middle: orientations of the generating LRPC; Left: distributions of pp; Right: distributions of ph.
Fig 9.
Reconstructions of the microflows in a copy of the LRPC located at a selected point of the liver tissue specimen.
a),b) velocity fields in the precapillary vessels of the PV and HV systems. c),d) Sinusoidal flow.
Fig 10.
Towards realistic lobular structures.
Left: The aggregate of 4 LRPC consisting of two portal lobules enables to create a larger periodic unit (the dark gray area), to consider nonuniform perturbations of the regular periodic structure which can comprise hexagonal and pentagonal hepatic lobulae (right).